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ICSE Class X Question Bank 2025 : Mathematics

7 pages, 91 questions, 3 questions with responses, 3 total responses,    0    0
Sanmesh Shriyam
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SEPTEMBER 2024 MATHEMATICS QUESTION BANK Std.10 This paper consists of 7 printed pages. Question 1 Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.) (i) The solution set for the linear inequation -8 x 7 < - 4, x I is (a) {x: x R, -1 x < 3} (b) {0, 1, 2, 3} (c) {-1, 0, 1, 2, 3} (d) { -1, 0, 1, 2} (ii) If a rectangular sheet having dimensions 22 cm x 11 cm is rolled along its shorter side to form a cylinder. Then the curved surface area of the cylinder so formed is: (a) 968 cm2 (b) 424 cm2 (c) 121 cm2 (d) 242 cm2 (iii) A ladder is leaning against a vertical wall. The ladder is 10 meters long and forms an angle of 45 degrees with the ground. How far up the wall does the ladder reach? (a) 5 2 (b) 5 3 (c) 2 (d) 2 2 (iv) In the given graph, the modal class is the class with frequency: (a) 72 (b) 21 (c) 48 (d) 36 1 (v) Assertion (A): Company X declared a dividend of 12% on its shares. Reasoning(R): The dividend declared by a company is directly proportional to its profitability and the number of shares held by each shareholder. (a) Both A and R are true, and R is the correct explanation of A. (b) Both A and R are true, but R is not the correct explanation of A. (c) A is true, but Ris false. (d) A is false, but R is true. (vi) Find the coordinates of the centroid of triangle ABC with vertices A(2,4), B(6,1) and C(8,5). (a) (15.5,10/3) (b) (3,0) (c) (16/3,3) (d) (16/3,10/3) (vii) Samir deposited 500 per month for 18 months in a bank's recurring deposit account. If the bank pays interest at the rate of 8% per annum, then find the interest earned by Samir during this period. (a) 570 (b) 750 (c) 500 (d) 400 (viii) If 3 is a root of the quadratic equation x2 px + 3 = 0 then p is equal to: (a) 4 (b) 3 (c) 5 (d) 2 (ix) The average weight of a group of 20 people is 70 kg. If the average weight of 10 of them is 65 kg and another group of 5 people has an average weight of 75 kg, find the average weight of the remaining 5 people. (a) 70 kg (b) 75 kg (c) 67 kg (d) 67.5 kg (x) If ABC DEF, AB=5 cm, BC=10 cm, EF=8 cm, and DF=13 cm, find the length of side DE. (a) 4 cm (b) 2 cm (c) 12 cm (d) 3 cm (xi) Point M (4, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, -5). Find the values of a and b . (a) (2, 6) (b) (2, 1) (c) (3,1) (d) (0,3) 2 (xii) tan 1 2 is equal to: (a) cos (b) sin (c) tan (d) cot (xiii) 1 3 ] + 3[ 0 1 (a) 3,8 (b) 5,8 (c) 8,5 (d) 5,13/3 If 2 [ 3 9 ]=[ 2 15 7 ],Find the values of x,y. 8 (xiv) Statement 1: 3x2 6x + 3 = 0 has real roots. Statement 2: The quadratic equation ax2 + bx + c = 0 have real roots if discriminant D<0. Which of the following is valid? (a) Both the statements are true. (b) Both the statements are false. (c) Statement 1 is true and statement 2 is false. (d) Statement 1 is false and statement 2 is true. (xv) If x <y then 1 _______ 1 (a) < (b) (c) (d) > Question 2 (i) A = {x : 11x- 5 > 7x + 3, x R}and B = {x : 18x - 9 < 15 + 12x, x R }. Find the range of set A B and represent it on a number line. [Ans: {x/x 4, x R} (ii) Use the factor theorem to factorize completely: x3+ x2 - 4x - 4. . [Ans: (x+1) (x +2) (x -2) (iii) In the diagram given above, AC is the diameter of the circle, with centre O. CD and BE are parallel. Angle AOB = 80 and angle ACE = 10 . Find: (a) Angle BEC, (b) Angle BCD, (c) Angle CED. [Ans: Angle BEC 500, Angle BCD= 1000, Angle CED =300 ]. Question 3 (i) Given [ ]M = 6I, where M is a matrix, and I is unit matrix of order 2x2. 3 (a) State the order of matrix M. (b) Find the matrix M. [Ans: 2x2 , [ ] (ii) Shirish buys 70 shares available at Rs 125 (par value Rs 100). (a) How much is his investment? (b) If the dividend is 7.5%, what will be his annual income? (c) If he wants to increase his income by Rs 105, how many extra shares should he buy? . [Ans: Rs 8750 , Rs525, 14] (iii) Use graph paper for this question. (a) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both axes. (b) A' is the image of A when reflected in the x axis. Write down the coordinates of A' and plot it on the graph paper. (c) B' is the image of B when reflected in the y axis, followed by reflection in the origin. Write down the coordinates of B' and plot it on the graph paper. (d) Write down the geometrical name of the figure AA'BB'. (e) Name two invariant points under reflection in the x axis. Question 4 (i) Manit deposits Rs 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity if the rate of interest is 6 % per annum. [Ans: Rs 6811.20] (ii) The median of the following observations 11, 12, 14,18, (x + 4),30,32,35,41 arranged in ascending order is 24. Find x and find the Mean. [Ans: x= 20, mean =23.67] (iii) The line joining P (- 4, 5) and Q (3, 2), intersects the y axis at R. PM and QN are perpendiculars from P and Q on the X axis. Find: (a) the ratio PR: RQ. (b) the coordinates of R. (c) the area of the quadrilateral PMNQ. [Ans: (a) 4:3 (b) (0,23/7) (c) 24.5 sq unit] Question 5 (i) (ii) A(1, 4), B(3, 2) and C(7, 5) are the vertices of a ABC. Find: (a) the coordinates of the centroid G of ABC. (b) the equation of a line, through G and parallel to AB. [Ans: (a) (11/3, 11/3) (b) 3x +3y =22] Using Componendo and Dividendo solve for x: 2x +2 + 2x 1 2x +2 2x 1 =3 [Ans: x =5/6] (iii) In the figure given below, P is a point on AB such that AP : PB = 4: 3. PQ is parallel to AC (a) Calculate the ratio PQ : AC, giving reasons for your answer;(b) In ARC, ARC = 90 and in PQS, PSQ = 90 . Given QS = 6 cm. Calculate the length of AR. [Ans: 3:7 , 14] 4 Question 6 (i) Prove: sin 2sin 3 = tan 2cos3 cos (ii) In the figure AB = AC = CD, ADC = 38 . Calculate: (a) ABC (b) BEC [Ans: (a) ABC =76 (b) BEC =28 ] (iii) The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45 to 30 . Find the height of the tower, correct to two decimal places. [Ans:13.66 m] Question 7 (i) Draw a histogram from the following frequency distribution and find the mode from the graph: Class 0-5 Frequency 2 5-10 5 10-15 18 15-20 14 20-25 8 25-30 5 (ii) Prove sin + cos sin cos 2 + = sin cos sin + cos 1 2cos 2 (iii) In the diagram given above, ABCD is a cyclic quadrilateral in a circle with centre O. If ADC = 130 ; find BAC. [Ans: BAC = 400 ] Question 8 (i) Using the properties of proportion, solve for x, given [Ans: 2 or / ] 5 + = (ii) In the given figure, AB and DE are perpendiculars to BC (a) Prove that ABC ~ DEC. (b) If AB = 6 cm, DE = 4 cm and AC = 15 cm. Calculate CD. (c) Find the ratio of the area of BC: area of DEC. [Ans: CD =5, 9:4] (iii) The mean of the following distribution is 52 and the frequency of class interval 30-40 is f . Find f . Class Interval Frequency 10-20 5 20-30 3 30-40 f 40-50 7 50-60 2 60-70 6 70-80 13 [Ans: f = 4] Question 9 (i) (ii) The volume of a conical tent is 2156 m3 and the area of the floor is 616 m2. Calculate the (a) radius of the base (b) height of the tent (c) length of canvas required to cover the tent if the width is 2 m.( Give your answer to the nearest m) [Ans: r =14, h = 10.5 , length of canvas = 385 m] If b is the mean proportion between a and c, show that: (iii) + + + + = From window A, 10 m above ground the angle of elevation of the top C of a tower is x , where tan x = 5/2 and the angle of depression of the foot D of the tower is y , where tan y = 1/4. Calculate the height CD of the tower in meters. [Ans: 110 m] Question 10 (i) A cylindrical can with a base radius of 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate (a) the total surface area of the can, in contact with water when the sphere is put in it. (b) the depth of water in the can before the sphere was put into the can. (Take =22/7) [Ans: (a) 192.5 cm2 (b) 2 ] (ii) Using a graph paper, draw an ogive for the following distribution which shows a record of weights in kg of 200 students. Weights (in kg) No. of students 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 5 17 22 45 51 31 20 9 6 Use your ogive to estimate: (a) the median weight. (b) the weight above which the heaviest 30% of the students fall. (c) the number of students who are overweight, if 55.7kg is considered as standard weight. Question 11 (i) The given block is made of two solids: a cone and a hemisphere. If the height and the base-radius of the cone are 24 cm and 10 cm respectively and the diameter of the hemisphere is 10 cm; find the total surface area of the block. (Take = 3.14) [Ans: TSA = 1208.9 cm2 ] (ii) Amidst the chilling whispers of a werewolf hunting Baskerville Hall, Sherlock Holmes, from a 100 m tower, notices a beast with a 450 angle of depression. If the beast is moving at 5 m/s, how much time Sherlock has before the figure reaches the tower's base? [Ans: 20 s] -------------------------------------------------------------------------------------------------------------Answers: Question 1 (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv) (xv) d d a a a d a a b a 7 b b c c d

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